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Fellow of the Royal Society (1998), Recipient of the American Society of Civil Engineers’ Maurice A Biot Medal (2020)

Harvard Wallace-Noyes Fellowship (2014), Caltech Postdoctoral Prize Fellowship in Theoretical Physics (2006-2009), National Science Foundation Graduate Research Fellowship (2000-2004)

Imperial College Teaching Fellowship (1996),  Imperial College Excellence in Teaching  (1996), Rector`s Medal for Outstanding Contribution to Teaching Excellence (2010), Fellow of the Royal Meteorological Society since (1968) 

SIAM Activity Group on Linear Algebra Best Paper Prize (2024), IMA Leslie Fox Prize for Numerical Analysis (2nd prize, 2021)

Distinguished Researcher Award, University of Utah (2017), Fellow of the Society for Industrial and Applied Mathematics (2016), Royal Society Wolfson Research Merit Award (2009), Royal Society Leverhulme Trust Research Professorship (1999)

Excellence in Innovation in Teaching award (2023), Royal Society Wolfson Research Merit Award (2012-2018), CMFT Young Researcher Award at the Computational Methods and Function Theory conference (2009), Philip Leverhulme Prize (2004)

Faculty of Natural Sciences Prize for Excellence in Teaching (2022)

London Mathematical Society Anne Bennett Prize (2019), Royal Society University Research Fellowship (2015-2020), Imperial College President’s Award for Outstanding Early Career Researcher (2018), Imperial College FoNS Prize for Excellence in Teaching (2016), "Freundeskreis der Tu Kaiserslautern" award for outstanding PhD (2010)

FoNS Prize for Excellence in Equality, Diversity and Inclusion (2024), The Wilkinson Prize for Numerical Software (2015)

Scholarship grant from Science without Frontiers Program of CAPESERC (2012), Los Alamos National Laboratory Achievement Award (1997), Fellow of Los Alamos National Laboratory (1988),  National Award of Excellence for Significant Contribution to the Nuclear Weapons Program (1984)

Leslie Fox 2nd Prize (2017), ANZIAM Cherry Ripe Prize (2013), Adams Prize (2012), Carl–Erik Fröberg Prize (2012), Leslie Fox Prize in Numerical Analysis (Second Prize, 2007)

Elected Fellow of the American Physical Society (2016), Fellow of the Institute of Mathematics and its Applications (since 2005). Harlan J. Perlis Award for Research, State of New Jersey (2002), NASA Group Achievement Award, ICASE Fluid Dynamics Group (1993)

APS Outstanding Referee of the Physical Review and Physical Review Letters journals, American Physical Society (2009)

Awarded the paper of the year 'Towards a Bifurcation Theory for Nonautonomous Difference Equations' by the International Society of Difference Equations (2006)

President's Award for Research Supervision (2017)

John Ockendon Prize (2024), Outstanding Referee for Journal of Fluid Mechanics (2023), Frenkiel award for Fluid Mechanics (2021), Wolf Foundation prize for doctoral ÌìÃÀ´«Ã½ (2014)

Invited Speaker - International Congress of Mathematicians in Hyderabad (2010)

Invited Speaker - International Congress of Mathematicians (2014), Elected Corresponding Member of the Dutch Royal Academy of Science (1999)